In the most commonly studied matching applications, e.g., onotlogy matching, any two concepts can be mapped independently of their positions in the graph structure they belong to. However, there are applications, such as matching of database schemas and first-order terms, where matching must preserve cetrain structural properties of the graphs being considered. The goal of this paper is to provide a solution to a new matching problem, that we call structure preserving matching, which could be defined as the problem of finding a mapping between those nodes that corrspond semantically to each other, still preserving a set of structural properties of the graphs being matched. We present an exact and an approxmiate structure matching algorithm, which utilize the theory of abstraction as a formal basis and build upon the well known tree edit distance measures. We have implemented the algorithms and applied them to the web service composition scneario. The preliminary evaluation results show its high efficieincy and effectiveness.